What is the derivative of (4x^2+7x^5/(sqrt(x))) ?

The derivative of (4x^2+7x^5/(sqrt(x))) is (3sqrt(x)(7x^3+4))/2+21x^{7/2}

What is the first derivative of (4x^2+7x^5/(sqrt(x))) ?

The first derivative of (4x^2+7x^5/(sqrt(x))) is (3sqrt(x)(7x^3+4))/2+21x^{7/2}

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\frac{d}{d x} (\frac{4 x ^{2} + 7 x ^{5}}{x})

\frac{3 x ( 7 x ^{3} + 4 )}{2} + 21 x^{\frac{7}{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} + 7 x ^{5}}{x})

Simplify

\frac{4 x ^{2} + 7 x ^{5}}{x} : x^{\frac{3}{2}} (7 x^{3} + 4)

= \frac{d}{d x} (x^{\frac{3}{2}} (7 x^{3} + 4))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{3}{2}}, g = 7 x^{3} + 4

= \frac{d}{d x} (x^{\frac{3}{2}}) (7 x^{3} + 4) + \frac{d}{d x} (7 x^{3} + 4) x^{\frac{3}{2}}

\frac{d}{d x} (x^{\frac{3}{2}}) = \frac{3 x}{2}

\frac{d}{d x} (7 x^{3} + 4) = 21 x^{2}

= \frac{3 x}{2} (7 x^{3} + 4) + 21 x^{2} x^{\frac{3}{2}}

Simplify

\frac{3 x}{2} (7 x^{3} + 4) + 21 x^{2} x^{\frac{3}{2}} : \frac{3 x ( 7 x ^{3} + 4 )}{2} + 21 x^{\frac{7}{2}}

= \frac{3 x ( 7 x ^{3} + 4 )}{2} + 21 x^{\frac{7}{2}}

x \to 0 lim (\frac{2}{2 x})

\frac{d v}{d t} = 9.8 - 1.2 v

\int_{0}^{1} - 6 (x^{2} + 1) e^{- x} d x

\frac{d}{d x} (200 e^{- x^{2} - 3 y^{2} - 9 z^{2}})

\frac{\partial}{\partial y} (x^{2} y)

What is the derivative of (4x^2+7x^5/(sqrt(x))) ?
The derivative of (4x^2+7x^5/(sqrt(x))) is (3sqrt(x)(7x^3+4))/2+21x^{7/2}
What is the first derivative of (4x^2+7x^5/(sqrt(x))) ?
The first derivative of (4x^2+7x^5/(sqrt(x))) is (3sqrt(x)(7x^3+4))/2+21x^{7/2}